The expression is equivalent to the 360[tex]k^2[/tex] - 48k
Given the Expression :
8k5∙9k−2(6k2)2
It means
(8k × 5) × 9k - 2(6k × 2) × 2
Now, Multiply the monomials
360[tex]k^2[/tex] - 2(6k × 2) × 2
Again, Multiply the monomials,
= 360[tex]k^2[/tex] - 48k
Hence, The expression is equivalent to the 360[tex]k^2[/tex] - 48k
What is Monomial ?
A monomial is a polynomial, which has only one term. A monomial is an algebraic expression with an single term but can have multiple variable and a higher degree too.
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9. Find an infinite set A such that a. A is finite and b. A is infinite. Use the real numbers R as the universal set.
Please show work.
An infinite set is infinite from start to end, but both sides can have continuity, unlike a finite set, which has both start and end elements. The finite() function in R Language is used to determine whether or not the elements of a vector are Finite values. It returns a Boolean value for each vector element.
What exactly is a finite number?A countable number less than infinity that is the cardinality of a finite set - that is, some natural number, possibly zero. A genuine number, such as the result of a measurement (of time, length, area, etc.)In other words, it is a set that can be finished counting. 1,3,5,7, for example, is a finite set with four elements. The finite set element is a natural number, i.e. a non-negative integer. A set is infinite if it has an infinite number of elements; finite if the elements can be counted.In R, there are two kinds of infinity. Inf and -Inf represent positive and negative infinity, respectively, whereas NaN stands for 'Not a Number.'Hence, The finite() function in R Language is used to determine whether or not the elements of a vector are Finite values.
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During an experiment, the temperature of a liquid, in degrees Celsius, is given by the function t(m)= -0.2m+6, where m is the number of minutes since the experiment began.
Which graph correctly shows this function?
The graph of the linear function t(m) = -0.2m + 6 is given at the end of the answer.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which:
The coefficient m is the slope of the function, which is the constant rate of change of the linear function.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the y-axis, and can also be interpreted as the initial value of the function.In this problem, the function is defined by:
t(m) = -0.2m + 6.
Hence:
The slope is of m = -0.2.The intercept is of b = 6.To graph the function, we have to consider the constraint that the time cannot be negative, hence the domain is:
t ≥ 0.
Thus, the graph is given by the image at the end of the answer.
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A theater group made appearances in two cities. The hotel charge before tax in the second city was $500 higher than in the first. The tax in the first city was 6.5% and the tax in the second city was 6% The total hotel tax paid for the two cities was $748.75. How much was the hotel charge in each city before tax?
Based on the taxes in the first city and the tax in the second city as well as the total hotel tax paid in the two cities, the hotel charge for each city before taxes was:
First city - $5,750Second city - $6,250How to find the hotel charge?The hotel charge before taxes was $500 higher in the second city than in the first. Assuming the charge in the first city was x, the charge in the second city was:
= x + 500
The total charge in the first city would be:
0.065x + 0.06(x + 500) = 748.75
0.065x + 0.06x + 30 = 748.75
0.125x + 30 = 748.75
0.125x = 748.75 - 30
0.125x = 718.75
x = 718.75/0.125
x = $5,750
The total charge in the second city would be:
= 5,750 + 500
= $6,250
In conclusion, the charges in the first and second cities are $5,750 in the first city and $6,250 in the second city.
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Round to the place value of the underlined digit 698, 07 to the underline number is six
The place value of the underlined digit (6) is tens of thousands and should be rounded to 70,000.
What is a place value?A place value simply refers to a numerical value (number) which denotes a digit based on its position in a given number and it includes the following:
TenthsHundredthsThousandthsUnitTensHundredsThousands.Tens of thousands.Hundred of thousandsIn this scenario, the place value of the underlined digit (6) is tens of thousands and 9 is the next digit to six (6). Therefore, we would add one (1) to the underlined digit (6) and then change all of the other digits to zero (0) as follows:
69,807 = 70,000
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HELPPPPP
How can we guarantee that a polynomial is not a perfect square, considering just the constant term? For instance, in 4, the constant term is -121, in 2, the constant term is 36. Which of them cannot be a perfect square and why, based only on the constant term?
Answer:
Polynomials with a negative constant term are not perfect squares, hence polynomial 4, with constant term of -121, is not a perfect square.
What are perfect square expressions?
Perfect square expressions are formed in two ways, either with the square of the sum or the square of the subtraction, as follows:
Square of the sum: (a + b)² = a² + 2ab + b².
Square of the subtraction: (a - b)² = a² - 2ab + b².
The constant term is the final term. Since this term is squared, it will always be positive for perfect squares, hence if the constant term is negative, it will guarantee that the polynomial is not a perfect square.
For the expressions in this problem, we have that:
The expression with a constant term of 36 can be a perfect square, as 36 is a positive number.
The expression with a constant term of -121 cannot be a perfect square, as -121 is a negative number.
Hope this helps :)
Step-by-step explanation:
Please Help
this is math, PLEASE HELP
A statement of order that shows the relation of the in-town speed limit to the highway speed limit is that the in-town speed limit is less than or equal to 30 and the highway speed limit is less than or equal to 60.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.
The rules for writing an inequality.In Mathematics, these four rules are generally used to write an inequality:
When the arrow points to the right on a number line, the inequality is either (≥ or >).When the arrow points to the left on a number line, the inequality is either (≤ or <).The circle/dot on a number line should be filled when the inequality symbol is (≥ or ≤).The circle/dot on a number line should not be filled when the inequality symbol is (> or <).Now, we would apply the aforementioned inequality rules to write the solution to the compound inequality shown in the graph above:
30 ≤ x ≤ 60.
In conclusion, x represent the speed limit for in-town and highway.
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URGENT!! ILL GIVE
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POINTS!!!!!
A metal sculpture has a total volume of 1250 cm³ and a mass of 9.2 kg.
Work out its density, in grams per cubic centimetre (g/cm³).
Give your answer to 2 d.p
Answer:
7.36 g/cm3
Step-by-step explanation:
Density = mass ÷ volume
Mass in grams = 9200g
Volume in cm3 = 1250cm3
9200 ÷ 7850 = 7.36
7.36 is already in 2 d.p.
What’s the slope of this line?
X
6
9
15
21
у
-5
-7
-11
-15
Slope is [tex]\frac{-2}{3}[/tex] of coordinates (6,5) and (9,-7).
What is slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. [1] The letter m is frequently used to represent slope; however, there is no obvious reason for this. The slope of a curve at a point in differential calculus is defined as the slope of the tangent line at that point as a generalization of this practical definition. The slope can be determined between any two locations when the curve is represented by a series of points in a diagram or list of point coordinates. Maybe when the curve is represented as a continuous function.
Given Data
coordinates - (6,-5) and (9,-7)
slope of the line denoted as m
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
m = [tex]\frac{-7-(-5)}{9-6}[/tex]
m = [tex]\frac{-2}{3}[/tex]
Slope is [tex]\frac{-2}{3}[/tex]
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How would I answer and what would be the answer?
Given the exression:
[tex]\frac{x-1}{x+4}-\frac{4x-11}{x+4}[/tex]Let's solve the expression and identify the error.
Since both expressions have the same denominator, let's combine the numerators:
[tex]\frac{(x-1)-(4x-11)}{x+4}[/tex]Apply distributive property:
[tex]\begin{gathered} \frac{x-1-4x-(-11)}{x+4} \\ \\ \frac{x-1-4x+11}{x+4} \end{gathered}[/tex]Combine like terms in the numerator:
[tex]\begin{gathered} \frac{x-4x-1+11}{x+4} \\ \\ \frac{-3x+10}{x+4} \end{gathered}[/tex]The error in the problem was that distributive property was not applied when the numerators were combined.
ANSWER:
[tex]\frac{-3x+10}{x+4}[/tex]6 plus 8 divided by 2
Using the PEMDAS ( In order to know the order of the operations)
P = Parentheses
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction
Accordint to this, we need to divide first, and then we need to add the resultant number, so:
[tex]\begin{gathered} 6+8\div2=6+4=10 \\ \\ \end{gathered}[/tex]Answer:
10
According to a 2017 survey conducted by the technology market research firm The Radicati Group, U.S. office workers receive an average of 121 e-mails per day (Entrepreneur magazine website). Assume the number of e-mails received per hour follows a Poisson distribution and that the average number of e-mails received per hour is five.
a) Probability of receiving no e-mails during an hour = 0.0067
b) Probability of receiving at least three e-mails during an hour = 0.8754
c) Expected number of e-mails received during 15 minutes = 1.25
d) Probability that no e-mails are received during 15 minutes = 0.2865
Given that five emails are typically received every hour. If X represents the number of emails received in an hour, then X is poisoned with the given parameter, λ = 5.
⇒ P (X = x) = [tex]\frac{e^{ -x} X^{x}}{x!} = \frac{e^{-5} 5^{x}}{x!}[/tex]
(a) Likelihood of not receiving any emails for an hour = p (x = 0)
= (e⁻⁵5⁰) / 0! = (e⁻⁵ * 1) / 1 = e⁻⁵ = 0.00674 ≈ 0.0067
(b) Likelihood of receiving three or more emails in a single hour P(x ≥ 3)
= 1 - [P (x < 3) = 1 - [P(x = 0) + P(x = 1) + P(x = 2)]
= 1 - [(e⁻⁵5⁰) / 0! + (e⁻⁵5¹) / 1! + (e⁻⁵5²) / 2!]
= 1 - [0.00674 + 0.03369 + 0.08422]
= 1 - 0.12465
= 0.87535 ≈ 0.8754
(c) The number of emails that should be received in the next 60 minutes = an hour's worth of emails on average = 5
As a result, the anticipated quantity of emails received in 15 minutes = 5 / 4 = 1.25
(d) Number of emails received on average every 15 minutes = Number of emails that should be received in the next 15 minutes = 1.25
Let X represent how many emails were received in 15 minutes. X then proceeds with a parameterized Poisson distribution, λ = 1.25
⇒ P (x = X) = [tex]\frac{e^{-x} X^{x} }{x!} = \frac{e^{-1.25}1.25^{x} }{x!}[/tex]
The likelihood that no emails will be received during the next 15 minutes = [tex]\frac{e^{-1.25}* (1.25)^{0} }{0!} = \frac{e^{-1.25}*1 }{1} = e^{-1.25} = 0.2865[/tex]
COMPLETE QUESTION: According to a 2017 survey conducted by the technology market research firm The Radicati Group, U.S. office workers receive an average of 121 e-mails per day (Entrepreneur magazine website). Assume the number of e-mails received per hour follows a Poisson distribution and that the average number of e-mails received per hour is five.
a. What is the probability of receiving no e-mails during an hour (to 4 decimals)?
b. What is the probability of receiving at least three e-mails during an hour (to 4 decimals)? For this question, if calculating the probability manually make sure to carry at least 4 decimal digits in your calculations.
c. What is the expected number of e-mails received during 15 minutes (to 2 decimals)?
d. What is the probability that no e-mails are received during 15 minutes (to 4 decimals)?
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Jacob and Diego are racing to see who can get his community service hours for scouting completed first. Jacob, who has already completed 50 hours, plans to volunteer for 5 hours per week going forward. Diego hasn't started yet, but plans to dedicate 6 hours per week to his volunteer project from now on. Before too long, the boys will be tied, with the same number of volunteer hours. How long will that take?
Number of weeks required before Jacob and Diego will be tied in the race to complete community service hours for scouting is equal to 50 weeks.
As given in the question,
Let number of weeks be represented by a variable x.
Jacob plans to devote 5 hours per week from now onwards. Hence his volunteer hours will cumulate to 5x+50 as he has already completed 50 weeks.
Diego plans to devote 6 hours per week from now onwards. Hence his volunteer hours will cumulate to 6x.
For Jacob and Diego to tie in the race, their volunteer hours should be equal. Translating this into a linear algebraic equation,
6x = 5x+50
=> 6x-5x = 50
=> x = 50
Therefore, number of weeks required before Jacob and Diego will be tied in the race to complete community service hours for scouting is equal to 50 weeks.
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Simplify the expression:
a^-2
1/[tex]a^{2}[/tex] is the answer.
How to simplify the expression?Given,
a^-2
Solution:
a^-2
Expand it
a^-2 = 1/a^2
= 1/[tex]a^{2}[/tex]
Therefore,
a^-2 = 1/[tex]a^{2}[/tex]
1/[tex]a^{2}[/tex] is the answer.
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Need help with Stats homework, Picture has been uploaded of the question
Solution:
Given that a livestock company reports that the mean weight of a group of young steers is 1123 pounds with a standard deviation of 84 pounds, this implies that
[tex]\begin{gathered} \mu=1123 \\ \sigma=84 \\ \end{gathered}[/tex]A) Percentage of steers that weigh over 1300 pounds.
Step 1: Evaluate the z score value.
The z score value is expressed as
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ where \\ x\Rightarrow sample\text{ value} \\ \mu\Rightarrow mean\text{ value} \\ \sigma\Rightarrow standard\text{ deviation of the sample} \end{gathered}[/tex]In this case, x equals 1300.
Thus, the z score value is evaluated as
[tex]\begin{gathered} z=\frac{1300-1123}{84} \\ \Rightarrow z=2.107142857 \end{gathered}[/tex]Step 2: Evaluate the probability that the steer would weigh over 1300 pounds.
Using the normal distribution table, we have
thus,
[tex]\begin{gathered} Pr(z>1300)=0.0175525991947 \\ \end{gathered}[/tex]The percentage of young steers that weigh over 1300 pounds is thus evaluated as
[tex]\begin{gathered} 0.0175525991947\times100 \\ =1.7552991947\% \\ \approx1.8\%\text{ \lparen1 decimal place\rparen} \end{gathered}[/tex]B) Percentage of steers that have weights under 1050 pounds.
Step 1: Evaluate the z score value.
Thus, we have
[tex]\begin{gathered} z=\frac{1050-1123}{84} \\ =-0.869047619 \end{gathered}[/tex]Step 2: Evaluate the probability that the steer would have weights under 1050 pounds.
Using the normal distribution table, we have
thus,
[tex]Pr(z<1050)=0.192410542709[/tex]Thus, the percentage of young steers that would have weight under 1050 pounds is evaluated as
[tex]\begin{gathered} 0.192410542709\times100 \\ =19.2410542709\% \\ \approx19.2\%(\text{ 1 decimal place\rparen} \end{gathered}[/tex]C) Percentage of young steers that weigh between 1000 and 1200 pounds.
Step 1: Evaluate the z score value.
[tex]\begin{gathered} z_1=\frac{1000-1123}{84} \\ =-1.464285714 \\ z_2=\frac{1200-1123}{84} \\ =0.9166666667 \end{gathered}[/tex]Step 2: Evaluate the probability that the steer would weigh between 1000 and 1200 pounds.
Using the normal distribution table, we have
thus, we have
[tex]Pr(1000Thus, the percentage of young steers that weigh between 1000 and 1200 pounds is evaluated as[tex]\begin{gathered} 0.748783381404\times100 \\ =74.8783381404\% \\ \approx74.9\% \end{gathered}[/tex]Find the measure of <1, <2, and <3.
The measure of the angles for the given parallel lines are-
∠1 = 100°∠2 = 80°∠3 = 100°What is defined as the term linear pair?Once two lines intersect at a single point, a linear pair of angles is formed. If the angles are adjacent to one another after the two lines intersect, they are referred to as linear. The sum of the angles of a linear pair always is 180°. These angles are also referred to as supplementary angles. The adjacent angles include those that share a vertex. As a result, the linear angles get a common vertex here as well.For the given question;
The set of parallel lines are given;
Thus,
∠1 + 80 = 180 (linear pair)
∠1 = 100°
Now, two set of parallel line form a parallelogram.
Thus, in parallelogram opposite angles are equal.
∠1 = °∠3 = 100°
So, ∠3 = 100°
And, ∠2 = 80° (opposite angle of 80)
Thus, the measure of the angles are calculated.
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Una masa de 2,0 kg está unida al extremo de una cuerda de 5,0 m. La masa se mueve en una trayectoria circular sobre una superficie horizontal sin rozamiento. Si la resistencia a la rotura de la cuerda es 40 N, la máxima velocidad lineal con la que se puede hacer girar la masa sin que se rompa la cuerda es aproximadamente
La maxima velocidad lineal de la masa con la que se puede girar la masa es igual a 40 newtons.
¿Cuál es la velocidad lineal máxima permitida por la masa en movimiento circular uniforme?
En este problema tenemos el caso de una masa (m), en kilogramos, conectada a una cuerda y que experimenta un movimiento circular uniforme, en donde la partícula describe un movimiento a velocidad lineal constante (v), en metros por segundo, debido a una aceleración radial que está en la forma de tensión (T), en newtons, a través de la cuerda. En consecuencia, la velocidad máxima permitida es determinada a partir de las leyes de Newton:
T = m · (v² / R)
Donde:
m - Masa, en kilogramos.v - Velocidad lineal, en metros por segundo.R - Longitud de la cuerda, en metros.Si sabemos que m = 2 kg, R = 5 m y T = 40 N, entonces la maxima velocidad lineal permitida es:
40 N = (2 kg) · v² / (5 m)
v = 10 m / s
La maxima velocidad lineal permitida es igual a 10 metros por segundo.
ObservaciónBrainly no dispone de suficientes problemas en español sobre el movimiento circular uniforme.
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Which of the following is LEAST associated with human capital?
a)medical treatment that reduces time off of work due to illness or injury.
b)maintenance of fully automated production facilities
c)a college course in accounting
d)an on-the-job training course in the latest production methods.
Answer:
Hope it helps you
Step-by-step explanation:
(a) medical treatment that reduces time off of work due to illness or injury.
Newton had 15 baseball cards. Today he bought 3 packs of baseball cards. Now he has a total of 45 baseball cards. Write and solve an equation to determine how many baseball cards were in each pack
Answer:
15 I did 15+15+15 or 15x3 and it equals 45
Step-by-step explanation:
Brainliest?
15
Divide 45 by 3 because newton has 15 base ball cards and each card has fifteen card in each pack
4. Solve the quadratic equation x² = 16.
[tex]x^2=16\\\sqrt{x^2}=\sqrt{16}\\x=\lm+/-4[/tex]
x = 4, x = -4
find slope of the line that passes through each pair of points 4,3 -1,6
Answer:
Formula for slope is given as (y2-y1) ÷ (x2-x1) or (y1-y2) ÷ (x1-x2), where x and y are the coordinates of the points.
Slope = (6 - 3)÷(- 1 - 4)
= -3/5
Describe the rate of change for the function f (x)=[tex]\sqrt{x}[/tex]
The rate of change is [tex]\frac{1}{2\sqrt{x} }[/tex]
What is rate of change ?The link between one quantity changing in respect to another is given by the rate of change formula.can be used to calculate the rate of change from y coordinates to x coordinates (x2 - x1 ). The rate of change m for a linear function is written as y=mx+b in the slope-intercept form for a line, whereas the rate of change for a function is written as (f(b)-f(a))/b-a. It is said that the rate at which one quantity changes in relation to another is known as the rate of change function. The amount of change in one item is simply divided by the comparable amount of change in another when calculating the rate of change.
Given that : The function f (x)=[tex]\sqrt{x}[/tex]
f (x)=[tex]\sqrt{x}[/tex]
[tex]f^{'} x = \frac{1}{2\sqrt{x} }[/tex]
The rate of change is [tex]\frac{1}{2\sqrt{x} }[/tex]
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A member of a book club wishesto purchase two books from aselection of eight booksrecommended for a certainmonth. In how many ways canshe choose them?Note: Crnn!r!(n-r)!
From a total of 8 books, she has a choice of 2 in 28 different ways.
What is permutation and combination ?When things are of diverse kinds, the term "permutation" is used to describe the various arrangements that could be made. Combination, meanwhile, is the quantity of smaller groups or sets that can be created from the components of a bigger set.
The member must select 2 books from a group of 8 books in the scenario that is provided. It is not important what sequence you select your books in. If a member chooses books A and B or books B and A, for instance, she is choosing the same books from the list of available titles (A,B,C,D,E,F,G, and H). By extension, this is a problem of combinations since the order of the selections is irrelevant in this situation.
Eight books, two at a time, must be combined to produce
The general formula of combination is :
[tex]nC_{r} = \frac{n!}{r!(n-r)!}[/tex]
Using the values of n=8 and r=2, we get:
[tex]8C_{2}[/tex] = [tex]\frac{8!}{2!(8-2)!}[/tex]
=28
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hihihihihiihiihihihihihihhi
Jessica makes $24,000 a year, butreceives weekly paychecks. If 12% ofher check is withheld for federaltaxes, what is her required weeklydeduction, including FICA?
The weekly deduction, including FICA is a $60
Define percentage.
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%"
Given,
Jessica makes in a year = $24000
She receives weekly pay checks is = 12%
We know, in 1 month there are 4 weeks and for 12 months there are 48 weeks.
so, Jessica makes per week = $24000 / 48
= $500
And, we know Jessica receives 12% paychecks then,
find, 12% of weekly payment
⇒12% of 500
⇒ (12 * 500) / 100
⇒$60
Hence, The weekly deduction, including FICA is a $60
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a final exam in math 160 has a mean of 73 with standard deviation 7.2. if 22 students are randomly selected, find the probability that the sample mean of their test scores is less than 75
The probability is that the mean of their test scores is less than 70.
What is probability?
A probability is a number that reflects tha chance of particular event will occur.
Sol-
As per the question given-
Mean = 73
Standard daviation=7.2
Number of students randomly selected =22
Let's take n number for experiment of outcomes.
The number of favorable outcomes can be denoted by x.
The formula to calculate the probability is -
probability = favorable
Outcomes/total outcomes =x/n
The number of standard daviation form the mean is called z.
Z = (x-¥)/€
Z=(75-73)(7.2/√22)
Z= -37.0582965
P(z<-37.05)
= 37.05
There for the probability is 37.05.
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pleaseee helpp meeee
Given:
The given expression is,
[tex]25^x[/tex]Required:
To select the equivalent expression.
Explanation:
if a population has a mean of 30, if 3 points are added to each score how do you calculate the mean for the new distribution
When the population has a mean of 30, if 3 points are added to each score, the mean for the new distribution is 33.
How to illustrate the information?It should be noted that mean simply means the average of a given set of numbers that are given. The entire group about whom you want to make conclusions is referred to as a population. The particular group from which you will gather data is known as a sample. The sample size is always smaller than the population as a whole. A population in research doesn't usually refer to humans.
In this case, the population has a mean of 30 a and 3 points are added to each score.
In this case, the new mean will be the addition of the numbers. This will be illustrated as:
= 30 + 3
= 33
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A) What is the probability that a 13-card bridge hand contains i) All 13 hearts? ii) 13 cards of the same suit? iii) Seven spades and six clubs?
Using the hypergeometric distribution, the probabilities are given as follows:
a) All 13 hearts: [tex]1.57 \times 10^{-12}[/tex]
b) 13 cards of the same suit: [tex]6.30 \times 10^{-12}[/tex]
c) Seven spades and six clubs: [tex]5.4 \times 10^{-9}[/tex]
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
Parameter x is the number of successes.Parameter N is the size of the population.Parameter n is the size of the sample.Parameter k is the total number of desired outcomes.The general parameters in this problem are given as follows:
N = 52, as a standard deck has 52 cards.n = 13, as 13 cards will be chosen.In item i, there are 13 hearts in a standard deck, hence k = 13 and the probability is P(X = 13), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 13) = h(13,52,13,13) = \frac{C_{13,13}C_{39,0}}{C_{52,13}} = 1.57 \times 10^{-12}[/tex]
For item ii, we consider the same context of item i, just now we can consider any of the four types of cards, hence:
[tex]p = 4 \times 1.57 \times 10^{-12} = 6.30 \times 10^{-12}[/tex]
For item iii, we want:
Seven spades from a set of 13.Six clubs from a set of 13.Hence the probability is given as follows:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 7) = h(7,52,13,13) = \frac{C_{13,7}C_{13,6}}{C_{52,13}} = 5.4 \times 10^{-9}[/tex]
More can be learned about the hypergeometric distribution at https://brainly.com/question/24826394
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Y=x when x increases by 5 what does y increase by